Correlators, Feynman diagrams, and quantum no-hair in deSitter spacetime

Abstract

We provide a parametric representation for position-space Feynman integrals of a massive, self-interacting scalar field in deSitter spacetime, for an arbitrary graph. The expression is given as a multiple contour integral over a kernel whose structure is determined by the set of all trees (or forests) within the graph, and it belongs to a class of generalized hypergeometric functions. We argue from this representation that connected deSitter $n$-point vacuum correlation functions have exponential decay for large proper time-separation, and also decay for large spatial separation, to arbitrary orders in perturbation theory. Our results may be viewed as an analog of the so-called cosmic-no-hair theorem in the context of a quantized test scalar field. This work has significant overlap with a paper by Marolf and Morrison, which is being released simultaneously.

arXiv comment57 pages, Latex, several figures. v2: more details given on derivation of parametric formula in sec.5, and exponential decay result in sec. 6, references added, figures added, typos removed

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Cited by in corpus (7)

• Massless interacting quantum fields in deSitter spacetime
• Infrared dynamics of the massive ${\varphi }^4$ theory on de Sitter space
• Non-linear sigma model in de Sitter space
• Physical momentum representation of scalar field correlators in de Sitter space
• QFT in the flat chart of de Sitter space
• On memory in exponentially expanding spaces
• Non-equilibrium evolution of quantum fields during inflation and late accelerating expansion